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Geol. Mag. 122 (5), 1985, pp. 555-568. Primed in Great Britain 555

Postcumulus processes in layered intrusions

R. S. J. SPARKS,* H. E. HUPPERT, f R. C. KERR,f D. P. McKENZIE* , & S. R. TAIT*

* Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, U.K.t Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, U.K.

(Received 30 November 1984; accepted 18 March 1985)

Abstract - During the postcumulus stage of solidification in layered intrusions, fluid dynamicphenomena play an important role in developing the textural and chemical characteristics of thecumulate rocks. One mechanism of adcumulus growth involves crystallization at the top of thecumulate pile where crystals are in direct contact with the magma reservoir. Convection in the chambercan enable adcumulus growth to occur to form a completely solid contact between cumulate andmagma. Another important process may involve compositional convection in which light differentiatedmelt released by intercumulus crystallization is continually replaced by denser melt from the overlyingmagma reservoir. This process favours adcumulus growth and can allow adcumulus growth withinthe pore space of the cumulate pile. Calculations indicate that this process could reduce residualporosities to a few percent in large layered intrusions, but could not form pure monomineralic rocks.Intercumulus melt may also be replaced by more primitive melt during episodes of magma chamberreplenishment. Dense magma, emplaced over a cumulate pile containing lower density differentiatedmelt may sink several metres into the underlying pile in the form of fingers. Reactions between meltand matrix may lead to changes in mineral compositions, mineral textures and whole rock isotopecompositions. Another important mechanism for forming adcumulate rocks is compaction, in whichthe imbalance of the hydrostatic and lithostatic pressures in the cumulate pile causes the crystallinematrix to deform and intercumulus melt to be expelled. For cumulate layers from 10 to 1000 metresin thickness, compaction can reduce porosities to very low values (< 1 %) and form monomineralicrocks. The characteristic time-scale for such compaction is theoretically short compared to the timerequired to solidify a large layered intrusion. During compaction changes of mineral compositionsand texture may occur as moving melts interact with the surrounding matrix. Both compaction andcompositional convection can be interrupted by solidification in the pore spaces. Compositionalconvection will only occur if the Rayleigh number is larger than 40, if the residual melt becomes lowerin density, and the convective velocity exceeds the solidification velocity (measured by the rate ofcrystal accumulation in the chamber). Orthocumulates are thus more likely to form in rapidly cooledintrusions where residual melt is frozen into the pore spaces before it can be expelled by compactionor replaced by convection.

1. Introduction

In recent years the physical ideas embodied in cumulustheory have been re-examined. Detailed studies of anumber of major layered intrusions have recognizedfield relationships that appear inconsistent with acrystal settling model (Campbell, 1978; Morse, 1979;McBirney & Noyes, 1979; Irvine, Keith & Todd, 1983;Wilson & Larsen, 1985). There are good arguments infavour of an in situ crystallization mechanism,although textural evidence for crystal settling is stillcompelling in some rocks, such as the Rhumperidotites (Brown, 1956; Tait, 1985). Despite theuncertainties that currently exist on the origin of theserocks, the cumulus classification survives. This isbecause Wager & Deer (1939), Wager, Brown &Wadsworth (1960) and Jackson (1961) recognized thatmany of the rocks from layered intrusions consist ofan initial crystal framework with interstitial porematerial. Those rocks with a substantial proportion ofpore material can be termed orthocumulates. Thoserocks with little or no surviving pore material can betermed adcumulates and those with intermediate

amounts can be called mesocumulates. Thus thecumulate classification is appropriate irrespective ofthe mode of formation (Irvine, 1982).

Postcumulus processes, which occur after thedevelopment of the initial cumulus framework(Wadsworth, 1985), can involve either completesolidification or recrystallization under subsolidusconditions. Several ideas on postcumulus processeshave recently emerged, partly based on experimentalinvestigations and theoretical advances in the fluiddynamical aspects of crystallization, porous mediaconvection and compaction of partially molten rock.Much of the data and detailed analyses on these ideasare contained in Kerr & Tait (1985a, b), in theunpublished Ph.D. theses of R. C. Kerr and S. R. Tait(University of Cambridge, 1984) and in recent work oncompaction (McKenzie, 1984, 1985; Richter &McKenzie, 1984). Important concepts have come fromMorse (1969, 1979, 1982) and Irvine (1980), based onstudying the petrography and chemistry of the rocks.Recent investigations of layered intrusions, in par-ticular on Rhum, have suggested that postcumulusprocesses are more diverse and complicated than

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556 R. S. J. SPARKS AND OTHERS

originally envisaged in the classic cumulus theory (forexample Young, 1984; Butcher, Young & Faithfull,1985; Tait, 1985; Young & Donaldson, 1985). Thispaper provides a synopsis of these new ideas andconcentrates on fluid dynamical phenomena that arelikely to be associated with consolidation of the porespaces and compaction of the matrix.

Although this paper is not specifically concernedwith Rhum,athe authors felt that it is appropriate toinclude a review of postcumulus processes in thisspecial issue. Rhum has had a central role indeveloping cumulus theory (Brown, 1956; Wager,Brown & Wadsworth, 1960). Several papers in thisvolume illustrate that Rhum continues to inspireimaginative new research into the origin of layeredrocks. In particular the issue highlights the importanceof intercumulus melt circulation which has also beenemphasized in the experimental and theoretical studiesreported here.

2. Cumulus theory

The theory of Wager, Brown & Wadsworth (1960) wasbased on the concept of crystal settling and ideasconcerning postcumulus processes originally conceivedby Hess (1939, 1960). At the orthocumulate extremethey envisaged rapid accumulation of crystals whichtrapped interstitial liquid. During subsequent equil-ibrium crystallization the trapped pore liquid couldreact continuously with the cumulus crystals to formlower temperature solid solutions. Some cumulusminerals, notably plagioclase, are slow to equilibrateand may become chemically zoned. Eventually newphases nucleate and grow in the pore space. Theadcumulate extreme was thought to occur underconditions of slow crystal accumulation. The cumuluscrystals were thus able to maintain chemical com-munication with the main magma reservoir bydiffusion of components through the interstitial melt,and thus could grow at constant composition untilvirtually all the pore space was eradicated. Wager,Brown & Wadsworth (1960) recognized the difficultyof static diffusion being a viable mechanism deep in thecumulate pile and argued that adcumulus growthwould be most effective in the uppermost layer of thecumulate pile. These ideas assumed that compactionwas unimportant (Wadsworth, this volume) and thatthe consolidation of cumulate piles was essentially acementation process.

As recognized by Morse (1979,1982), the distinctionbetween cumulus crystals and pore material can beretained without implying a sedimentary origin for thecumulus framework. If the rate of in situ growth ishigh, then crystals may form a relatively openframework containing trapped melt. On the otherhand if the solidification rate is low then there couldbe time for adcumulus growth by chemical diffusionto occur at the topmost layer of cumulus grains in

direct contact with the magma. In the extreme case, thedistinction between cumulus crystal and pore materialloses meaning since the model does not necessarilyinvolve the formation of a network of poressurrounded by a crystal framework. By the envisagedprocess, a sharp, well-defined interface developsbetween totally solid adcumulate rock and the mag-ma. However, as Wadsworth (this issue) has pointedout, there is evidence that adcumulus growth can occurwithin cumulate piles, so a model of adcumulus growthat the interface between the magma and the floor maynot be the only mechanism operating in nature. Amodel of adcumulus growth by static diffusionbetween pores deep within the cumulus pile and thechamber is physically implausible (Wager, Brown &Wadsworth, 1960; Hess, 1972; Tait, Huppert &Sparks, 1984). Thus, alternative mechanisms to thatinvolving adcumulus growth at the magma-solidinterface are required.

Workers on layered intrusions have long recognizedthe important role of convection (Wager & Deer, 1939;Morse, 1969). Recent developments in fluid dynamicshave, however, recognized a number of new physicalphenomena, which may have an important influenceon the evolution of layered igneous rocks. Crystal-lization from a saturated solution often involvesvigorous convective motions which can stronglyinfluence how solidification occurs (Chen & Turner,1980; Huppert & Sparks, 1984). These effects couldinfluence events both at the interface of the cumuluspile with the magma and within the pore space deepwithin the pile. In addition, Irvine (1980) hasrecognized geological features which suggest thatcompaction is an important process. McKenzie (1984,1985) and Richter & McKenzie (1984) demonstratedthat in a partially molten system the crystalline matrixcan deform, resulting in two-phase flow, extraction ofpore liquid and compaction of the matrix. These lattertheoretical studies confirm that compaction is muchmore effective than was formally thought and shouldbe an important factor in the formation of layeredintrusions. In the following sections we assess howfluid dynamical ideas are likely to influence theinterpretation of cumulate rocks.

3. Compositional convection

When a crystal grows from a liquid a thin film orboundary layer of melt is formed adjacent to thecrystal faces. This film is depleted in chemicalcomponents taken into the crystalline solid andconsequently there is a compositional and hence adensity gradient across the film. Under suitableconditions the film will be dynamically unstable andcan convect away. Several studies have argued thatsuch compositional convection will be of majorimportance in magma chambers (Morse, 1969; Chen& Turner, 1980; McBirney, 1980; Huppert & Sparks,



Postcumulus processes in layered intrusions 557

1984). The relevance of this process for cumulate rocksis that convection is a much more effective way thanstatic diffusion of maintaining a constant meltcomposition adjacent to a growing crystal face.Compositional convection and perhaps thermalconvection may consequently be major factors inenabling adcumulus growth to occur.

3.a. Dynamical principles

During crystallization from a basaltic melt changes indensity are usually dominated by compositional effects(Morse, 1969; Sparks & Huppert, 1984). In crystal-lization of olivine and pyroxene, for example,residual melts become lower in density despite thedecrease in temperature. When plagioclase is a majorcrystallizing phase, the residual melt often becomesdenser. Such compositional convection is generallydominant over motions that might be induced bypurely thermal effects.

In the case of crystallization on the floor of a magmachamber or within the underlying cumulate pile,experimental and theoretical studies (reviewed byHuppert & Sparks, 1984) suggest a limited number ofarrangements. In one situation crystallization canrelease heavy liquid which must sink or simply remainadjacent to the crystal if the underlying material

contains even heavier liquid or is impermeable. Inother situations, where compositional effects dominate,crystallization can lead to the release of light residualfluid at or beneath the chamber floor which canconvect away to be replaced by heavier liquid from thechamber. Figure 1 shows an experiment in which anaqueous solution of CuSO4 and Na2SO4 is beingcooled from below. Crystals of CuSO4.5H2O andNa2SO4.10H2O are growing within a basal layer ofglass balls underlying a large reservoir of the solution.As the crystals grow, thin streams of solute-depletedfluid emerge from the porous medium and rise to mixwith the overlying reservoir. Continuity requires thatan equal flux of solute-enriched solution descendsinto the porous media. Adcumulus growth ofCuSO4.5H2O and Na2SO4.10H2O crystals is takingplace between the glass balls.

Several fundamental points concerning compos-itional convection should be noted:

(i) Vigorous compositional convection can occuralthough the system is thermally stable, as illustratedin the experiment where the fluid is being cooled frombelow. The compositional effects on solution densityoverwhelm the stabilizing temperature gradient.

(ii) The convective patterns can sometimes be quitedifferent in compositional convection to those observedduring thermal convection. For example, in thermal

Figure 1. Streams of light residual fluid are rising from a bed of glass balls (0.5 cm diameter) in which crystallization ofCuSO4.5H2O and Na2SO4.10H2O is taking place. The photograph shows a width of 5 cm.

36 GEO 122




convection caused by uniform heating of a surface,motions can be quite chaotic at high Rayleigh numberswith rapid horizontal mixing. In compositionalconvection each crystal provides the source of a verythin uprising plume or stream. The motion isdominantly vertical with limited horizontal mixing dueto the much lower chemical diffusivity in comparisonto thermal diffusivity.

(iii) The appropriate boundary layer thicknesses areproportional to the relevant coefficient of diffusion andare hence much less for compositional convection thanfor thermal convection. Compositional boundarylayers next to growing crystal faces can be as little astens or hundreds of microns. This latter type ofconvection can therefore more readily operate in smallpores.

(iv) The experiments show that adcumulus growthcan occur within a porous medium and need not beconfined to the uppermost layers of a cumulate pile.

3.b. Interface between the magma and cumulate pile

The idea that adcumulus growth can occur directly onthe floor of the chamber is supported by experimentalstudies. We have carried out a number of experimentsin which an aqueous solution with a non-eutecticcomposition is cooled from either the roof or floor of

the container. In some experiments a solid' adcumulate'region made of interlocking crystals forms with a sharpinterface against the overlying liquid.

Figure 2 shows a case where CuSO4.5H2O andNa2SO4.10H2O crystals grew to form an impermeablelayer on the surface of a bed of glass balls. The systemwas being cooled from below, and crystals nucleatedthroughout the porous medium and on its uppersurface. However, the permeability of the porousmedium was sufficiently low that compositionalconvection was weak within the pore space. Light,residual fluid released from crystals that nucleated onthe upper surface could convect away much morerapidly than the fluid released from crystals within theporous medium. Consequently, the crystals on theupper surface continued to grow as they were suppliedwith solute-rich solution by vigorous compositionalconvection that took place above. The CuSO4-Na2SO4

layer contained no ice and is effectively a pureadcumulate. Thus, in some circumstances, adcumuluscrystal growth can be more effective on the surfacethan in the interior of the porous medium.

We have conducted experiments with a wide varietyof aqueous systems in which cooling and crystallizationoccurs at the floor of a tank containing anhomogeneous fluid. Some of these experiments havebeen described by Kerr & Turner (1982) and Huppert

Figure 2. The photograph shows an impermeable layer of CuSO4. 5H2O crystals (dark) and Na2SO4.10HaO crystals overlyinga porous medium of 0.032 cm glass balls. The speckled appearance of the glass balls is due to many tiny crystals of CuSO4. 5H2Oand Na2SO4.10H2O which grew in the pores. In this experiment convection was weak (initial Rayleigh number 103). The scaleon the right is shown in centimetres.




& Worster (1985). For most systems in which light,water-enriched fluid is released by crystallization of theparticular salt compound, a solid layer of hydrated saltis formed with little or no ice. However, in experimentson the same systems carried out on the ice side of theeutectic, residual fluid denser than the original isreleased. In this case the dense fluid fills crevices andinterstices between the ice crystals and the solidproduct contains crystals of the salt as well as ice. Ingeological parlance these materials would have a moreorthocumulate character. The experimental studiessuggest that the density changes caused by crystal-lization on the surface of a chamber floor shouldhave an important influence on whether adcumulate'hardgrounds' can form in magma chambers.

Another factor, that cannot yet be investigated inthe tank experiments, is the influence of thermalconvection in a magma chamber. Vigorous thermalconvection could sweep away residual magma ofgreater density from the floor and replenish theenvironment of crystal growth with fresh magma topromote adcumulus growth. Morse (1969) invokes thisprocess in the formation of anorthosite layers in theKiglapait intrusion.

In summary, the concept that adcumulates mayform as a virtually solid 'hardground' on the base ofa magma chamber is plausible. As argued by Wager,Brown & Wadsworth (1960) and Morse (1979, 1982),this process should be most effective when theaccumulation or solidification rate is very slow.Experimental studies confirm that this mechanism willbe more effective if aided by compositionalconvection.

3.c. The interior of-the cumulate pile

Slumping of layers to depths of many tens ofcentimetres or metres (Jackson, 1961; Wadsworth,1985) and the occurrence of orthocumulates andmesocumulates with clear evidence of trapped melt(Wager & Brown, 1968) suggest that substantialdepths of porous material commonly form in magmachambers. Further, geochemical evidence for 'in-filtration metasomatism' (Irvine, 1980) and other datapresented by various authors (Butcher 1985; Butcher,Young & Faithfull, 1985; Palacz & Tait, 1985; Tait,1985; Young & Donaldson, 1985) imply thatcirculation of intercumulus melt can occur withincumulate piles. There is also evidence that adcumulusgrowth occurs within crystal piles. In the case ofRhum, the peridotites are considered to representrapid accumulations of olivine crystals followingreplenishment (Brown, 1956; Tait, 1985). The layersof loosely packed olivine crystals had perhaps 35%initial porosity and can be tens of metres thick. Asargued by Wadsworth (1985) and others, the porespace ultimately was filled by an assemblage ofplagioclase and clinopyroxene. The composition of the

interstitial material in the Rhum peridotite does notcorrespond to a sensible liquid and is partlyadcumulate in character. Thus, the 'hardground'model (outlined in Section 3.b) cannot be the onlymechanism of forming adcumulates.

Tait, Huppert & Sparks (1984) proposed thatintercumulus melt convection during pore-spacecrystallization could be a mechanism of adcumulusgrowth at some depth within cumulate piles. Thispossibility was also noted by Irvine (1980). To test thishypothesis further, Kerr & Tait (1985a) carried out aseries of experiments on crystal growth in a porousmedium using the Na2SO4-CuSO4-H2O ternarysystem. In the experiments a layer of glass balls orCuSO4 crystals (10 to 14 cm deep) was placed on thefloor of a circular perspex cylinder, 29 cm in diameterand 60 cm high. The tank was then filled with asolution nearly saturated in both Na2SO4 and CuSO4

and then cooled from below by passing coldmethylated spirits though a basal brass plate. Theexperiments involved systematic variations in startingcompositions, cooling rates and grain size andtherefore permeability of the porous media. Thedetailed results are described by Kerr & Tait (1985a)and here we only summarize the main observationsand conclusions.

Each experiment began with a porosity of about35 %. As cooling proceeded the solutions soon reachedsaturation and crystals of either CuSO4.5H2O,Na2SO4.10H2O or both nucleated within the porespaces. For those experiments with high permeability(large glass balls or crystals) and slower cooling rates,streams of light residual fluid were observed to emergefrom the upper surface of the porous media asillustrated in Figure 1. Eventually liquid trapped in thepore space reached the ternary eutectic temperature,and ice as well as CuSO4.5H2O and Na2SO4.10H2Oformed a well-defined solid layer at the base of the tank(Fig. 3 a). This entirely solid layer grew with time andmoved up through the porous medium until there wasan entirely solid, lower layer consisting of glass ballsand interstitial crystalline solid. The composition andtemperature of the overlying fluid was monitoredthroughout each experiment and the solid product wasalso analysed after each run. Estimates of theconvective velocities of plumes emerging from theporous medium were also made.

The main results of these studies are summarizedbelow:

(i) In those experiments where vigorous compos-itional convection was observed to come from theporous medium, the compositions of the finalinterstitial solid was enriched in CuSO4 and Na2SO4

in comparison to the initial homogeneous solution.Adcumulus growth had occurred and the process wasonly halted when ice nucleated in the pore space toform the eutectic solid layer.

(ii) The experiments with large balls (and therefore36-2




Figure 3. (a) The photograph shows the interior of a porous medium of 5 mm glass balls in which crystals of CuSO4. 5H2Oand Na2SO4.10H2O have grown. In the lower 25 cm of the tank a layer of totally solid ice and hydrated salt crystals has formedwith a sharp boundary with overlying ice-free porous medium, (b) The photograph shows dark poikilitic crystals ofCuSO4. 5H2O which have grown in a porous medium (d = 0.032 cm) and have enclosed several glass balls. The upper blacklayer is a capping layer as described in Figure 2.




higher initial permeability) showed the most vigorouscirculation and the greatest enrichment of the porematerial in CuSO4 and Na2SO4.

(iii) In an experiment with the smallest balls(diameter 0.32 mm) and lowest permeability, noconvection was observed and the pore material hada composition indistinguishable from the initialsolution.

(iv) In those experiments with only weak convectionan impermeable capping layer formed as shown inFigure 2.

(v) Textural features included development of'poikilitic' intercumulus CuSO4.5H2O crystals (Fig.3 b).

In order to apply these results and observations tomagma chambers a theoretical treatment of theconvection and crystallization in porous media is nowdeveloped. The occurrence of significant adcumulusgrowth by compositional convection requires thatseveral physical conditions are met. The first re-quirement is that crystallization produces lowerdensity residual melt so that compositional convectioncan take place on the floor. If denser residual fluid isproduced convection could still occur if there is a freshsupply of lower density fluid from beneath or evendenser fluid from above. However, for chambers asthey are conventionally perceived adcumulus growthwithin the cumulus pile is much more probable if lightresidual liquid is produced. Since the fractionalcrystallization of plagioclase-rich cumulate assem-blages is thought to generate dense residual melts(Sparks & Huppert, 1984), we anticipate that com-positional convection will be most effective in maficcumulates, where melt density decreases withfractionation.

A second requirement is that the solutal Rayleighnumber, Ras, exceeds a critical value of about 40(Lapwood, 1948). This parameter can be defined as

kghAp0)

where k is the permeability, g is the acceleration dueto gravity, h is the depth of the porous medium, /i isthe fluid viscosity, D is the effective chemical diffusivityin the fluid and Ap is the density difference in the liquiddriving the convection. Table 1 compares the rangesof physical properties and parameters encountered in

the experiments and estimates for magma chambers.For cumulate piles with initial porosities of 0.3 to 0.5and depths of 1-100 m the solutal Rayleigh numbersrange from 103 to 10', suggesting that compositionalconvection should be vigorous in magma chamberswhere low density residual liquids are being generated.

A third requirement concerns the relative rates ofconvection and solidification. As crystals fill the porespace, permeability decreases, and therefore theconvection velocity should be reduced. Eventually theresidual porosity should become sufficiently small thatthe pore fluid will freeze in situ before circulation couldtake place. In this situation the relative magnitudes ofthe solidification velocity (vs) and the convectivevelocities (vc) become important. In this context wetake solidification velocity to be the velocity at whichthe solid boundaries at the chamber margins moveinwards and is approximately the same as theaccumulation rate (Irvine, 1970). The convectionvelocity refers to the velocity of melt within the porespace. Figure 4 plots the initial and final porositiesagainst ball diameter in four of the experiments.Residual porosities were estimated by comparing thefinal solid compositions to the average solutioncompositions. A family of parallel curves indicates theapproximate value of the ratio of convection velocityto the solidification velocity. The hypothesis that wewished to test was that when vc/vs = 1.0 there wouldbe little further adcumulus growth because the porefluid is frozen in before significant circulation couldtake place. Figure 4 shows that in the experiments theresidual trapped porosity lies between the lines ofvc/vs = 1 and 10 when adcumulus growth effectivelyceased.

The characteristic convective velocities can beestimated (Kerr & Tait, 1985a) by the followingexpression

d2gApe4&

10/* '(2)

where e is the porosity, d is the grain diameter and Apis the difference between the densities of residual liquidand the original magma. Figure 5 shows the variationof convection velocity against magma viscosity ford = 0.2 cm, Ap = 10~a gm/cm3 and for cumulate pileswith porosities from 0.05 to 0.4. As demonstrated inthe experiments adcumulus growth is possible if the

Table 1. A comparison of the main parameters affecting compositional convection in the experimental system and in mafic and ultramaficcumulates

ParameterExperimental

valuesMagma chamber

values

Particle diameter d (m)Initial porosityPermeability k (m2)Depth of porous medium h (m)Viscosity /i (Pa s)Solutal diffusivity D (m2 s"1)

3 x 10-"-5 x 10-"0.35-0.4110-K-10-'0

0.110"3

10-"

5x 10-"-5xl0-2

0.310-5_l0-'»

1-102

1-10"2

io-"-io-13




BALL DIAMETER (mm)

Figure 4. A plot of porosity versus ball diameter for four experiments in the system CuSO4-Na2SO4-H2O. The numbers 1,3, 4 and 5 refer to individual experiments described by Kerr & Tait (1985a). Each experiment shows the initial porosity(subscript i) and the final residual porosity (subscript r). The diagram is contoured for the ratio of convective velocity (vc)to solidification velocity (vs).

convective velocity is greater than the solidificationvelocity.

For rapidly cooled bodies, such as sills or lava flowssolidification velocities are expected to be severalmetres per year or more. Adcumulus growth would notbe expected to be important in such bodies since thesolidification velocity exceeds the calculated convec-tion velocities even at large porosities (Figure 5). Inmedium sized shallow-level intrusions like Rhum,solidification velocities of order of 1 to 0.1 metres peryear would be anticipated (Irvine, 1970). Adcumulategrowth would be expected within the cumulus piles,but pure adcumulates would not be anticipated by thismechanism. Inspection of Figure 5 indicates thatresidual porosities of approximately 10% could beachieved if the convection velocity is 10"1 metres peryear with basaltic magma. Orthocumulates and

10'4 10"3 10'2 10'1 10° 10'

CONVECTION VELOCITY (m yr"1)

Figure 5. A plot of magma viscosity in Pa s versus convectivevelocity for different values of porosity. Each line is for adifferent value of porosity (e).

mesocumulates would be expected to form fromcumulate piles with high initial porosity.

In magma chambers that cool very slowly becauseof their great size or deep crystal level, adcumulusgrowth within the pile should be most effective.Inspection of Figure 5 suggests that residual porositiesof only a few percent could be achieved by thismechanism if the solidification and convective velo-cities are comparable at values of 1O~2 to 1O~4 m peryear. As in the 'hardground' model, interstitialadcumulus growth would also be expected to be moreprominent in deep and large intrusions.

3.d. Effects of magma chamber replenishment

The recognition that many magma chambers are opensystems, which may be either continuously orperiodically replenished by new magma, suggests thatthis process may also influence postcumulus evolutionand consolidation. In particular, replenishment canlead to the situation where primitive high densitymagma can be emplaced on the floor of the chamber(Huppert & Sparks, 1980) and can overlie lowerdensity magma within the cumulate pile. This fluiddynamically unstable configuration should lead to theheavy primitive magma sinking into the cumulus pileand lower density residual magma rising and mixingwith the overlying magma layer. This kind of processis believed to have occurred in the evolution of theRhum peridotites and allivalites (Huppert & Sparks,1980; Young, 1984; Tait, 1985; Palacz & Tait, 1985).

This process has been investigated by theoreticaland experimental studies (Kerr & Tait, 1985 ft). Figure



Postcumulus processes in layered intrusions

Figure 6. Photograph of an experiment in which a layer of slightly denser fluid is sinking into a porous medium of glass balls.A fingered interface develops. The fluids have equal viscosities (0.1 Pa s).

6 illustrates a typical experiment where a fluid (usuallya glycerine-water mixture) has been emplaced withina porous medium of glass balls until the level of thefluid is just level with the upper surface of the balls.A layer of slightly denser (typically by about 1 %) dyedfluid is then emplaced. In the photograph the heavierfluid has sunk into the porous medium in a series offinger-like protrusions. The heavy fluid progressivelyreplaces the interstitial light fluid which rises and mixeswith the overlying fluid reservoir. Dimensionalanalysis shows that the velocity of the fingers can beexpressed

v = •CkgAp

lie(3)

where C is a constant. Kerr & Tait (1985ft) haveinvestigated the effects of different viscosities anddifferent initial temperatures on the values of theconstant C.

Figure 7 summarizes the application of this workusing a typical experimental value of C = 0.55,d = 0.2 cm and Ap = 5 x 10~2 gm/cm3, which showshow the finger velocity varies with porosity andmagma viscosity. Typical calculated velocities rangefrom several metres/year to more than 100 metres/year.These values imply that new magma can penetratemany metres or even hundreds of metres into the

underlying cumulate pile, depending strongly on theporosity and to a lesser degree magma viscosities. Wenote that the velocities are generally higher than eithersolidification velocities or convective velocities cal-

L.>»

E

ILO

Ci

LJJ

NG

ER

i

100

10

1

/ 4y

I / //, />0-1 0 2 0 3

POROSITY0 4 0 5

Figure 7. Plot of finger velocity versus porosity for differentvalues of the magma viscosity, calculated from equation (3).In the calculations Ap = 500 kg/m3, d = 0.2 cm andC = 0.55.




culated in Section 3.b, so we infer that this kind ofexchange may be important in open system chambers.

In the experiments the glass balls are chemicallyinert and at the same temperature as the two fluids. Ina cumulate pile there are likely to be severalcomplications since the downward moving melt will beout of chemical and thermal equilibrium with thecrystalline framework. This situation may lead toprecipitation of new minerals, re-equilibration ofexisting phases (for example, modification of theFe/Mg ratio in olivine and pyroxene) or resorption.Mixing between the two melts could also occur andcould lead to precipitation of new phases (Young,1984). Tait (1985) describes in detail variations oftexture, modal abundances, mineral chemistry andisotope ratios in the Rhum peridotites and allivalitesof unit 10 that can be attributed to the sinking ofdenser magma into a cumulus pile with which it is outof chemical equilibrium. Another example of thisprocess appears evident in the Great Dyke inZimbabwe. Wilson (1982) describes harzburgite layersin cyclic units containing resorbed orthopyroxenecumulus grains and intercumulus olivine. The reactionof opx -> ol + SiO2 is apparently possible if thetemperature increases. One possibility is that hotprimitive magma with olivine on the liquidus sank intoan orthopyroxene cumulate pile and resulted inresorption of pyroxene and precipitation of inter-cumulus olivine.

4. Compaction

In explaining the spectrum of rock types fromorthocumulates to adcumulates most petrologists haveemphasized cementation processes rather than com-paction in which the interstitial melt is simply squeezedout by deformation of the crystalline matrix. Inprinciple this process could, for example, form amonomineralic 'adcumulate' rock without any ad-cumulus growth having taken place. A study of theMuskox intrusion by Irvine (1980) and a theoreticalanalysis of the compaction of partially molten rock byMcKenzie (1984, 1985) and Richter & McKenzie(1984) have provided arguments for compaction beinga major process in layered intrusions.

4.a. Magmatic infiltration metasomatism

Irvine (1980) observed that the boundaries betweenmajor cyclic units in the Muskox intrusion, defined bychanges in modal mineralogy, did not coincide withdiscontinuities in the chemical composition of minerals.Notably the abrupt changes in forsterite content ofolivine were displaced several metres above the contactbetween major olivine pyroxenite and dunite layers,whereas breaks in the nickel contents of olivinecoincided with the lithological boundaries. He arguedthat these relationships were caused by compaction of

the cumulate pile and upward flow of differentiatedintercumulus melt. This melt would necessarily reactwith surrounding olivine crystals causing them tobecome iron-rich. Irvine presented a detailed analysisof the chemical effects of this process and concludedthat the abrupt changes in mineral composition wouldbe preserved but displaced upwards with respect to themodal layering.

Richter & McKenzie (1984) have modelled quan-titatively the consequences of compaction of apartially molten layer on the chemistry of the matrixand fluid. They confirm that the kind of displacementsobserved by Irvine in the Muskox intrusion wouldindeed be the consequence of compaction.

4.b. Fluid dynamics of compaction

The theoretical analysis of compaction by McKenzie(1984, 1985) and Richter & McKenzie (1984) hasprovided the basis for assessing under what cir-cumstances compaction should be important inlayered intrusions. McKenzie (1984) has analysed thecompaction of a layer of partially molten rock withconstant porosity lying on an impermeable base. Forexample, this would be an appropriate model for alayer of loosely packed olivine cumulus crystalsrapidly formed after a replenishment event. The causeof compaction is that the intercumulus melt has alower density than the crystalline matrix. Thus thereis an imbalance between the lithostatic and hydrostaticpressure gradients. The imbalance results in two-phaseflow with compaction of the crystalline matrix andupward flow of the melt. In the case of a compactinglayer of constant porosity resting on an impermeablefloor McKenzie's analysis demonstrates that com-paction will begin at the base and the velocity ofescaping melt will increase upwards.

A fundamental parameter emerging from Mc-Kenzie's analysis is the compaction length scale, whichis the height over which the compaction rate decreasesby the factor e, and is defined

(4)(i

where £ and rj are the bulk and shear viscosities ofthe matrix, /i is the melt viscosity and k thepermeability. As McKenzie has discussed in detail,estimation of the matrix properties is uncertain.Richter & McKenzie (1984) used values of bulk andshear viscosities of 1018 Pa s. Experimental andtheoretical studies (McKenzie, 1985) indicate that thisvalue is appropriate for partially molten mantle. Theratio k//i could vary from as much as 10~n m3 kg"1 sin a layer of olivine with 30% porosity and a lowviscosity (1 Pa s) picritic liquid to as little as10"16 m3 kg"1 s in a cumulate layer containing highviscosity (50 Pa s) basalt and a porosity of 1 %. Thusthe compaction length scale might range from as much




as several kilometres to as little as 0.5 metresdepending on the values of the relevant parameters.These length scales could often be much less than thethicknesses of porous cumulate piles in the largemagma chambers represented by major layeredintrusions, implying that compaction should occur,provided that intercumulus cementation or freezingdoes not operate on shorter time scales.

For layers of cumulates with a thickness h that islarger than the length scale Sc, the velocity of fluid, w0,initially emerging out of the top of a layer of initiallyconstant porosity e can be expressed as

It(5)

where ps and pt are the densities of the crystallinematrix and intercumulus melt respectively. It shouldbe noted that (5) is strictly only valid at t = 0(Appendix B of McKenzie, 1984). However, w0 servesas a useful measure of the compaction rate, since it canbe compared with other characteristic velocities ofcompositional convection and solidification in amagma chamber.

The velocity of the melt in a partially molten layerof thickness h is zero at the base of the layer andincreases upwards. The initial velocity can becalculated from

—,60= ojn 1 -cosh (—

(6)

where w is the melt velocity and b) the matrix velocityat height z above the base. McKenzie (1985) deduceda characteristic time-scale for compaction:

(7)

Richter & McKenzie (1984) have obtained fullnumerical solutions to the time dependent problem ofa compacting layer of constant initial porosity. Aparticularly useful result concerns the time-scale, th,required to reduce the total amount of fluid in the layerby the factor e. For a layer of thickness h McKenzie(1985) has found that

tA=h_ **(8)

The time-scale th can thus be calculated for thetypical layer depths and physical conditions found inlayered intrusions and can be compared with thetime-scales of other processes such as solidificationand convection.

Some general conclusions relevant to the effectivenessof compaction in ultramafic cumulates can be reachedby considering the behaviour of olivine cumulatelayers of different thicknesses and initial porosities.The formation of such a simple porous layer is thoughtto be a common phenomenon in the formation ofultramafic cyclic units (Brown, 1956; Huppert &Sparks, 1980). In the calculations we have assumed aconstant viscosity of 3 Pa s, a matrix density of3200 kg/m3, a melt density of 2700 kg/m3 and a matrixbulk viscosity (£+|?/) of 1018 Pa s. In calculations ofpermeability we have followed the arguments ofMcKenzie (1984) and have used equation 4.4 in thatpaper and a grain radius of 1 mm. In the followingdiscussion the reader should be aware that there areconsiderable uncertainties in estimating both the bulkviscosity and the permeability of the matrix at lowporosities.

Table 2 lists some characteristic parameters for thecompaction of an olivine cumulate layer withintercumulus basaltic melt. For layers of the samethickness as the compaction length scale and theappropriate porosity value (as listed in Table 2) thetime-scale required to reduce the amount of inter-cumulus melt by e is approximately twice th. Thussignificant compaction can occur on time-scales of afew hundred to several thousand years. This resultshould not differ significantly for other kinds of maficcumulate rock, since none of the major controllingfactors, except porosity, are likely to vary greatly inmafic systems. The characteristic time-scale for theconductive cooling of a sheet of thickness la can beusefully compared to these time-scales and is defined

<c = - , (9)K

where K is the thermal diffusivity (8 x 10' m2 s"1). Fora 100 m thick sill tc = 100 years, which is a muchshorter time-scale than the 4200 years for a compactionlength scale of 98 m (Table 1). Thus compaction wouldhave no influence in such a thin intrusion because itfreezes too fast. For a 1 km thick sill, tc = 4 x 104 yearsand is comparable to the time-scales deduced for

Table 2. Characteristic parameters for the compaction of a partially molten layer of olivine and basaltic melt with viscosity of 3 Pa s. Notethat for a layer of thickness <5C the time-scale, /„, is twice T0.

0O fc(j//t(m3kg-'s) <Sc(m) T0 (years) w0 (m/yr)

0.30.10.030.010.003

1.80 x4.12 x9.57 x

3.3 x9.0 x

10"11

lO"13

1Q-15

10"16

io-'8

42436429818.23

9.38 x1.25 x2.10x3.63 x6.45 x

102

103

103

103

103

6.460.57

4.8 x 10~2

5.06 xlO"3

4.65 x 10"4




10 10 100 1,000

LAYER THICKNESS (m)

10,000

Figure 8. Compaction time scale, th, is plotted against layerthickness for molten layer of olivine and basaltic melt(/t = 3 Pa s). Curves are plotted for two values of porosity,e = 0.1 and e = 0.01.

0003

MELT VELOCITY (m/yr)

Figure 9. The velocity of liquid emerging from the top of acompacting layer is plotted against porosity for differentlayer thicknesses in metres. When Sc 4 h the single linea) = o>0 is appropriate. Approximate solidification velocitiesof three intrusions of different dimensions are indicated forcomparison.

values of layers less than 1000 m thick. Thuscompaction might become a factor in intrusions ofthis dimension. Finally, for a 5 km thick sill (com-parable to the stratigraphic thickness of several largelayered intrusions), tc = 1 m.y. which is clearly ordersof magnitude slower than time-scales deduced foreven layers a few metres thick with low porosity.Compaction may therefore be a very effective mech-anism of producing adcumulate rocks with lowresidual porosity in intrusions with dimensions muchgreater than 1 km. Large slowly cooled intrusionsshould show the most complete expulsion of inter-cumulus melt and the most extreme adcumulates.

The numerical calculations of Richter & McKenzie(1984) yield general results for the time-dependentcompaction of partially molten layers. As thethickness of the layer departs increasingly from 8C,resulting in either h > dc, or h <t Sc, the time scaleth for compaction will increase as is clear frominspecting equation (8). Figure 8 illustrates this effectby plotting the time-scale th against layer thickness fore = 0.1 and 0.01. The most rapid removal of inter-cumulus melt occurs for those layers of thickness Sc.

Figure 9 shows the variation of the velocity (w—6d)against porosity for different layer thicknesses. Eachcurve converges onto a single curve that is independentof h and corresponds to the limit h > Sc. The meltvelocities can be compared with the solidificationvelocities which characterize intrusions of differentsizes and cooling rates. If the solidification rate issignificantly faster than the melt velocity compactioncannot be important because the interstitial melt willbe frozen too quickly. In Figure 9 we consider threedifferent solidification rates, respectively appropriateto a 1 km thick sill, the Rhum intrusion and theStillwater Complex.

For a solidification rate of 1 m/year (as in a 1 kmsill) the melt velocity is always much less. Thus in alayer of cumulate comparable to the sill thickness thecompaction rate would be negligible in comparison tofreezing rates for a melt viscosity of 3 Pa s. In anintrusion of the size of Rhum or Skaergaard a typicalrate of solidification might be 10"1 m/year (Irvine,1970). For cumulate layers greater than 100 m thickcompaction should become a significant factor. Forfi = 3 Pa s, the compaction velocity is comparable toor greater than freezing velocities for layers withporosities of a few percent. For slowly cooled plutonssuch as the Stillwater or Great Dyke, solidificationvelocities might decrease to as little as 10~2 m/year.Compaction could become a significant factor in layersa few tens of metres thick. Very efficient expulsion ofintercumulus melt could be expected with residualporosities of less than 1 %. In large intrusionsadcumulate rocks are widespread and it appears likelythat compaction was an important process. Forexample the dunite layers of the Great Dyke (Wilson,1982) are almost pure monomineralic rocks (> 99%olivine).

4.c. Compaction and cementation

Cementation and compaction can occur together, butone of these processes may dominate the other indifferent situations. A quantitative assessment of theirrelative roles under different boundary conditions isnot yet possible, but some qualitative insights can begained from the experimental and theoretical workreported here.

Both processes may produce adcumulates but bothwill become insignificant if the solidification rate ishigh. Adcumulate rocks will therefore form if at least




one of the characteristic velocities of compaction andconvection substantially exceeds the solidificationvelocity. The following qualitative inferences on theirrelative importance can be made:

(i) Convection should dominate close to the top ofthe cumulate pile where the porosity is high and whereh is small compared to Sc.

(ii) Compaction should dominate in thick layers oflow porosity (h > So).

(iii) In any given layer in which compositionalconvection initially dominates at high porosities,compaction will eventually become dominant as theporosity decreases with time.

(iv) In the case of slowly cooled, closed systemmagma chambers, Morse (1982, personal commun-ication) has argued that extreme adcumulate rocks aregenerated at or close to the interface with the cumulatepile. This idea has been discussed in section 3.b wherelittle or no interstitial pore space is ever generated. Inthis situation compaction can have no role and Morseconsiders that the case for a deep crystal mush has tobe made in such intrusions. He argues that compactionis more probable in open systems where accumulationrate may be high. For the case of feldspathicadcumulate in slowly cooled intrusions diagnosticcriteria to distinguish extreme surface adcumulusgrowth from extreme compaction have not beendeveloped. Distinguishing the two models fromtextural or geological evidence is important andpresents an interesting challenge to petrologists.

4.d. Open-system effects

In open systems like Rhum the accumulation rate mayvary by orders of magnitude. For brief periodsfollowing a replenishment event, sedimentation ratesof olivine from a new layer of primitive magma couldbe as much as metres or even hundreds of metres peryear because of rapid crystallization in response toheat transfer between the liquid layers within thechamber (Huppert & Sparks, 1980). Then, followingsuch an episode, accumulation rates could return torates of order 10~2 m/year due to slow conductive heatloss. Thus wide variations of porosity might developwithin the cumulate pile under these circumstances.Scott & Stevenson (1984) and Richter & McKenzie(1984) have shown that layers of excess porosity in apartially molten rock can move as waves or pulses withrespect to the surrounding matrix and can break upinto several zones of high porosity with greaterstability. These waves would be expected to interactchemically with their surroundings and could producereplacement features by dissolving out some mineralsand reprecipitating others. Geological and geochemicaleffects that might be ascribed to this process have beendescribed by Irvine (1980) and Butcher, Young &Faithfull (1985).

5. Discussion

This paper reviews some of the ideas on the origin ofcumulate rocks, based on fluid dynamical principles.The final chemical and textural characteristics of arock appear to us to be strongly influenced by twomajor processes: convective circulation of melt aboveand within the cumulus pile, and compaction of thecrystalline matrix. Both processes involve movementof intercumulus melt and chemical interactionsbetween the melt and matrix. These processes can leadto changes in mineral compositions and textures as themelt re-equilibrates and reacts continually with itsmatrix. As illustrated by the studies of Irvine (1980),Tait (1985) and Palacz & Tait (1985) the mineralcompositions and isotopic propertiescan be profoundlymodified. Adcumulus growth, resorption, reactiontextures and replacement textures are likely to proveto be manifestations of intercumulus melt migrationand circulation.

The cumulate classification has proved to be usefuland resilient to changes in ideas. However, it is nowevident that there are several different ways ofgenerating an adcumulate rock. In particular expulsionof melt by compaction is recognized as an importantmechanism of generating adcumulate rocks. Achallenge for the future will be to recognize diagnosticcriteria which will enable the relative importance ofcementation and compaction in the evolution ofdifferent kinds of cumulate rock to be assessed. Giventhe richness of fluid dynamical and chemical pheno-mena that can take place in magma chambers webelieve that the terms in cumulate classification canonly be used in general descriptive sense. The terms canno longer have more than superficial genetic signi-ficance. Interpretation of cumulate rocks will thereforeincreasingly involve detailed arguments, constrainedby the textures, field relations and mineral composi-tions, that are made with reference to the physicalprocesses that can occur in magma chambers.

Acknowledgements. S.R.T. and R.C. K. acknowledgestudentships from N.E.R.C. and Trinity College, Cambridge,respectively. H.H. and R.S.J.S. are supported by the B.P.Venture Research Unit. We acknowledge detailed reviewsand comments on an earlier version of the manuscript byNeil Irvine, Tony Morse, Ian Parsons, John Wadsworth andRichard Wilson.

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